# The Ring is retarded to 0 rad/s

Consider a ring of mass $$m$$ and radius $$R$$ touching a rough wall of coefficient of friction $$\mu$$ as shown in figure. The ring has an initial angular velocity of $$\omega_0$$.

Find the time taken by the ring to come to a halt.

Details and Assumptions

• The ring doesn't translate on the wall.

• $$\mu = \dfrac{1}{\sqrt{3}}$$

• $$m = 1 kg$$

• $$R = 1 m$$

• $$\alpha = \dfrac{\pi}{3}$$

• $$\omega_0 = 10 rad/s$$

• $$g = 10 m/s^2$$

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